In an attempt to reduce the growth of its population, China instituted a policy limiting a family to one child. Rural Chinese suggested revising the policy to limit families to one son. Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl, and the successive births are independent, explain the following:

A) What would be the average family size?

B) What would be the ratio of newborn boys to newborn girls?

Answers

Answer 1

A) Average family size will be 2 children + 2 parents or a total of 4 people. B) Ratio of newborn boys to girls will be 1:1 For this, I will assume that each family will continue to have girl babies until a boy is born, then they will stop having children. So let's determine the number of girls that are born. 1/2 of all families will have a girl as their first child. 1/4 of all families will have a girl as their second child. 1/8 of all families will have a girl as their third child. The average number of girl children per family will be the limit of the infinite sequence 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/(2^n) where n approaches infinity. The limit to the above equation is 1. So on average there will be 1 girl per family. Now each family continues to have children until they get a boy. So each family will have 1 boy. So the average family size will be 2 children. Half the families will only have 1 boy, 1/4th will have 1 girl, and 1 boy, 1/8 will have 2 girls and 1 boy, etc. So the average family size is only 2 children. And the ratio of boys to girls will be 1 to 1 as expected if the birth of a boy is just as likely as the birth of a girl.

Related Questions

using the Pythagorean theogram find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long

Answers

Pythagorean Theorem is A^2 + B^2 =C^2. So, to find a leg instead of the hypotenuse you switch it around to C^2 - B^2=A^2. 10^2 - 8^2= the missing leg. 100- 64=C^2. 100-64=36. So then, you just square root the 36 which is 6. So 6 is the length of the other leg. And, if you want to you can take original Pythagorean Theorem and plug in all the numbers to double check.

The length of a leg of a right triangle is 6 feet.

Used the concept of Pythagoras's theorem states,

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that,

In a triangle, the other leg is 8 feet long and the hypotenuse is 10 feet long.

Let us assume that,

the length of a leg of a right triangle = x

Hence by using Pythagoras's theorem,

10² = 8² + x²

100 = 64 + x²

100 - 64 = x²

36 = x²

x² =36

x = √36

x = 6

Therefore, the length of the leg is 6 feet.

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solve for t q=(s+t)(r/2)

Answers

Isolate the factor (s+t): s+t = q / (r/2). This simplifies to s+t=2q/r.
Subtract s from both sides to isolate t:

t=2q/r - s (Answer).

Alternatively, mult. both sides of q=(s+t)(r/2) by 2 to eliminate the fraction r/2:

2q=(s+t)(r) = sr + tr

Subtract sr from both sides: 2q - sr = tr

Divide both sides by r to obtain an equation for t: (2q/sr) - (sr/r) = t,
or (2q/sr) - s = t

Which statement include two quantities in the real world that are additive inverses

Answers

Right answers: A hot-air balloon ascends 2000 ft from the ground and then descends 2000 ft.

Noa hiked 2 mi up a mountain trail and then hiked 2 mi down the trail.

what's the vertex and axis of symmetry of y=2x^2+8x+3 ?

Answers

well, the squared varaible is the "x", that means is a vertical parabola, so the axis of symmetry, will be x = "the x-coordinate of the vertex", whatever that coordinate happens to be, so let's check using the coefficients.

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ 2}}x^2&{{ +8}}x&{{ +3}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{8}{2(2)}~~,~~ 3-\cfrac{8^2}{4(2)} \right)[/tex]

A watermelon seed is 0.4cm long. How far would a line of 116 watermelon seeds stretch?

Answers

It would be 1.5 feet

116 * 0.4= 46.4cm
here hope this helps xx

the lengths of the sides of a triangle are consecutive odd integers.if the perimeter of the triangle is 27 what is are the lengths of all three sides?

Answers

The lengths of each side are 9

bearing in mind that, if you multiply any integer whatsoever, by 2, you get an even number, 3*2 or 17*2 or 4*2 and so on.

to get an ODD integer, simply hop once forward of backwards from any even integer, 2-1, or 2+1 or 8+1 or 8-1.

to get a consecutive ODD integer, simply hop twice from any odd integer, say 3+2, or 7+2 and so on.

now, let's pick a reference integer, say hmmm "a".

we know that a * 2, or 2a is an even integer, therefore (2a + 1) is an ODD integer, and (2a +1 ) + 2 is a consecutive odd integer. So, there you have it, our first two odd integers, and the next one, is, you guessed it, (2a + 1) + 2 + 2

so, our three odd consecutive integers are (2a+1), (2a+3) and (2a+5)

so, the triangle has a perimeter of 27, so, let's add them up then

[tex]\bf (2a+1)+(2a+3)+(2a+5)=27\implies 6a+9=27 \\\\\\ 6a=18\implies a=\cfrac{18}{6}\implies a=3[/tex]

so, our first odd integer is

2a + 1

2(3) + 1 --> 7

and surely you know what the other two are.

Felicia has a box of 16 cookies. if she divides all of the cookies up evenly among the 7 children she watches at the day care, how many cookies will each child get?

Answers

Each child will get 2 cookies,with two leftover. Technically 2.28, but rounding to a whole number is 2, because you wouldnt give a child .28 of a cookie lol

it is going to be 2 1/3

The gasoline gauge on a van initially read 1/3 full. When 10gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?

Answers

so it went from 1/3 full to 3/4 full when 10 gallons were put in, so.... what fraction is 10 gallons anyway? let's check the difference.

if say, when full is "x" gallons,

[tex]\bf \cfrac{3}{4}x-\cfrac{1}{3}x=10\implies \cfrac{9x-4x}{12}=10\implies \cfrac{5x}{12}=10\implies 5x=120 \\\\\\ x=\cfrac{120}{5}\implies x=24[/tex]

If mountain mack splits his week evenly between carving fishing lures and duck decoys, what is the maximum number of fishing lures and duck decoys he could carve?

Answers

Given the question:

Mountain Mark and Big Lake Bob spend their time carving fishing lures and duck decoys. The table below shows their production possibility schedule, which describes various combinations of fishing lures and duck decoys they each can carve efficiently in a week.

[tex]\begin{center} \begin{tabular} {|c {2.3cm}|c {2.3cm}|c {2.3cm}|c {2.3cm}|} \multicolumn {4} {|c|} {Production Possibility Schedules}\\[1ex] \multicolumn {2} {|c|} {Mountain Mark}&\multicolumn {2} {|c|} {Big Lake Bob}\\[1ex] Fishing Lures&Duck Decoys&Fishing Lures&Duck Decoys\\[1ex] 40&0&100&0\\ 32&10&80&6\\ 24&20&60&12\\ 16&30&40&18\\ 8&40&20&24\\ 0&50&0&30 \end{tabular} \end{center}[/tex]

If mountain mack splits his week evenly between carving fishing lures and duck decoys, what is the maximum number of fishing lures and duck decoys he could carve?

From the table it can be seen that in a full week, if mountain mack is carving fishing lures only, he can carve 40 fishing lures. This means that in half of a week, he can carve 20 fishing lures.

Similarly, from the table it can be seen that in a full week, if mountain mack is carving duck decoys only, he can carve 50 duck decoys. This means that in half of a week, he can carve 25 duck decoys.

Therefore, if mountain mack splits his week evenly between carving fishing lures and duck decoys, the maximum number of fishing lures and duck decoys he could carve are 20 fishing lures and 25 duck decoys.

Final answer:

To find the maximum number of fishing lures and duck decoys Mountain Mack can carve, we need to divide his available time equally between the two activities. The maximum number of each item he can carve depends on the total hours available, the time it takes to carve a fishing lure, and the time it takes to carve a duck decoy.

Explanation:

To find the maximum number of fishing lures and duck decoys that Mountain Mack could carve, we need to split his week evenly between the two activities. Let's say he has a total of 'x' hours available in a week. Since he'll be dividing his time equally, he'll spend 'x/2' hours carving fishing lures and 'x/2' hours carving duck decoys.

To put this in terms of fishing lures and duck decoys, we need to know the time it takes to carve each item. Let's say it takes 'y' hours to carve a fishing lure and 'z' hours to carve a duck decoy. The maximum number of fishing lures Mountain Mack can carve would be 'x/2y' and the maximum number of duck decoys he can carve would be 'x/2z'.

So, to find the maximum number of fishing lures and duck decoys Mountain Mack can carve, we need to know the total number of hours available in a week ('x'), the time it takes to carve a fishing lure ('y'), and the time it takes to carve a duck decoy ('z').

8 + 5y = 38 how to solve and check

Answers

Subtract 8 from both sides
5y=30

Divide both sides by 5
y=6

Check by plugging in to original equation
8+5(6)=38
8+30=38
True

Final answer: y=6

The value of a professional basketball player's autograph rose 30% in the last year. It is now worth $338.00. What was it worth a year ago?

Answers

338 x 0.30 = 101.4

338 - 101.4 = $236.60

Help me please I forgot my notes at school

Answers

1/2 x 6 = 3
3 x 8 = 24
24/6 = 4
4 - 1 = 3

3 is your answer

hope this helps

Because of BIDMAS, we know to do the brackets first
so it would be 3 * 8 ÷ 6 - 1
Division and multiplication next, so 4 -1
Lastly, subtraction
3

I am not 100% sure this answer is right but this is system I was taught
Hope it helped

How to do lond division 0.6÷0.0024

Answers

so...notice first off, the 0.6 has 1 decimal, the 0.0024 has 4 decimals

what happens is, the dot goes poof BUT, you need to add as many zeros to each number as the other's decimals.

the 0.6 has one decimal, so 0.0024 gets an added zero and loses the dot, to become 000240.

the 0.0024 has four decimals, thus the 0.6 gets added 4 zeros then, and loses the dot, to become 060000

and then you divided that, those are the dividend and divisor.

Final answer:

To divide 0.6 by 0.0024 using long division, adjust the numbers to remove the decimals, becoming 6000 divided by 24. The result of this division is 250.

Explanation:

To solve the problem of long division, specifically for 0.6 ÷ 0.0024, you need to adjust both numbers to remove the decimal points before division. Start by shifting the decimal point in each number. In this case, shift the decimal for both numbers 4 places to the right, resulting in 6000 divided by 24.

So, it becomes a simpler division problem: 6000 ÷ 24. When you divide 6000 by 24, the result is 250.

Therefore, the result of 0.6 ÷ 0.0024 is 250.

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You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 20 years?

Answers

The amount is @8358.7 and the interest is $3858.7.

Sage correctly found the following quotient. 1 1/2 divided by 1/3= 4 1/2 . (a) Create a model to show the quotient. (b) Explain what the half in the quotient refers to in your model

Answers

(a) for this you need to draw an example. Like a pizza or pie being cut.

(b) show that half of the quotient refers to Sage dividing the pizza/pie

When dividing 1 1/2 by 1/3, the quotient 4 1/2 indicates that each person receives half of a whole unit, which in our model is half of a pizza.

(a) To model the quotient 1 1/2 ÷ 1/3, imagine you have 1 1/2 units of something, like 1 1/2 pizzas. Now, if you divide each pizza into thirds, you'd have 3 halves of pizza. So, 1 1/2 pizzas divided by 1/3 pizza per person equals 4 people, each getting 1/2 of a pizza.

(b) The half in the quotient represents the portion of each whole unit (in this case, pizza) that each person receives. In our model, it signifies that each of the 4 people receives half of a pizza.

Please help answer this pre calc question

Answers

place the equation for g ( x^2-5) over the equation for f(4x+1)

so you get

x^2-5/4x+1

B is the answer

Casey has 8
1
2
yards of fabric. She uses 2
1
2
yards to make pillows and 3 yards to make curtains. How much fabric is remaining?

Answers

You have 812 total. 812 - 212= 600.
Then you have 600 yards and subtract 3 which would equal 597 yards of fabric.

How do you do number 24?

Answers

Answer: k = 4

---------------------------------------------
---------------------------------------------

Explanation:

The piecewise function is essentially two different functions joined together. In this case,

h(x) = kx if 0 <= x < 1
OR
h(x) = x+3 if 1 <= x <= 5

The value of x determines which piece we use.

The two pieces will join together to be continuous only if the y value is the same for x = 1.

Plug x = 1 into the first piece and we get
h(x) = k*x
h(1) = k*1
h(1) = k

Do the same for the second piece
h(x) = x+3
h(1) = 1+3
h(1) = 4

Set the two results (k and 4) equal to each other and we get k = 4.

Use the scale factor to find the area of the enlarged figure. Explain your steps.

Answers

well if you divide 25.6 by 8 and then multiply four by that answer then you have the answer for a, so 4 times 3.2=12.8 , and then you would multiply 25.6 and 12.8 which is 327.68

The area of the enlarged figure will be 327.68 square units

The scale factor will be the ratio of the similar sides of a rectangle.

For the given triangles, the required scale factors will be expressed as:

[tex]\frac{4}{8} =\frac{a}{25.6}\\\frac{1}{2} =\frac{a}{25.6}\\2a = 25.6\\a=\frac{25.6}{2} \\a=12.8[/tex]

Next is to get the area of the bigger rectangle:

[tex]Area = Length \times Width\\Area=a\times 25.6\\Area=12.8\times 25.6\\Area=327.68 units^2[/tex]

Hence the area of the enlarged figure will be 327.68 square units

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What is the value of x in the equation 2x + 3y = 36, when y = 6?

Answers

x is equal to the value of 9

the answer is x=9

i'm not good at showing my work, but I'm positive in my answer I'm an honors student.

2.85 as a mixed number

Answers

[tex]2.85=2+0.85=2+ \frac{85}{100} =2+ \frac{5*17}{5*20} =2+ \frac{17}{20} =2\frac{17}{20} [/tex]

I hope you got the idea

what is2.1e-10 in standard form

Answers

The number is basically saying 2.1*10^(-10)

The base is 2.1 and the exponent is -10. The exponent of -10 tells us to move the decimal point exactly ten spaces to the left and we will end up with the final answer 0.00000000021

Note: there are 9 zeros between the decimal point and the '2'

Finding the area shaded figure

Answers

complete square = 100 square yards

triangle = 1/2 x base x height = 1/2 x 10 x 5 = 25 square yards

100-25 = 75 square yards

shaded area = 75 square yards

What is 1 ten thousand + 19 thousands+ 2 tens+ 9 ones in standard form

Answers

The answer is 29029
10000+19000+20+9=29029

On a backpacking trip through Europe, Troy spent 20 Swiss francs to stay one night in a youth hostel. If the foreign exchange rate between the U.S. dollar and the Swiss franc is 1:2.2, how much did Troy spend in U.S. dollars?

Answers

Answer:

Troy spent $9.09.

Step-by-step explanation:

Troy spent 20 Swiss Francs to stay one night in a youth hostel.

1 U.S. Dollar = 2.2 Swiss franc

We have to convert 20 Swiss franc to U.S. dollars.

So we divide 20 by 2.2 to convert Swiss franc to U.S. dollars.

= [tex]\frac{20}{2.2}[/tex] = 9.09090909 ≈ $9.09

Troy spent $9.09 to stay one night in a youth hostel.

There is 2/5 cup of cream in a nelly cream pie.How much cream would you need if you were making 3/4 of a pie

Answers

(2/5) / 1 = x / (3/4).....2/5 cups to 1 pie = x cups to 3/4 pie
cross multiply
(1)(x) = (2/5)(3/4)
x = 6/20 which reduces to 3/10 cups <==

To make [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream. This calculation is done by multiplying [tex]\frac{2}{5}[/tex] cup (the amount required for a whole pie) by [tex]\frac{3}{4}[/tex].

To calculate the amount of cream needed for making [tex]\frac{3}{4}[/tex] of a nelly cream pie when the full pie requires [tex]\frac{2}{5}[/tex] cup of cream, we simply multiply these two fractions. To do this, first convert the mixed number [tex]\frac{3}{4}[/tex] to an improper fraction. We already have it in the proper format, so we can directly multiply:

([tex]\frac{2}{5}[/tex]) * ([tex]\frac{3}{4}[/tex]) = (2*3)÷(5*4) = [tex]\frac{3}{10}[/tex]

Therefore, for [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream.

rename the number.. 24 ten thousands

Answers

24 ten thousands is 24,000

Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?

First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.
How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.49.
How much does a reusable water bottle cost? About $10.
How long does a reusable water bottle last? Basically forever (or until you lose it).
How much does a water filter cost? How much water will they filter?
A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)
A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months
An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.

The cheapest option saves her $________ over a year.

Answers

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If sinθ = 3/4 and is in the first quadrant, then cosθ = _____.

Answers

The trick here is to recognize that "sin omega = 3/4" provides us with the length of the opposite side of a first-quadrant triangle and the length of the hypotenuse; they are 3 and 4 respectively.

Find the length of the adjacent side (x) using the Pythagorean Theorem: 3^2 + x^2 = 4^2, or x^2 = 16 - 9 = 7. Then the length of the adj. side, x, is sqrt(7).

The cosine of omega is adj / hyp, or sqrt(7) / 4.

Answer: The answer is [tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

Step-by-step explanation: Given that

[tex]\sin \theta=\dfrac{3}{4}[/tex] and [tex]\theta[/tex] is in Quadrant I.

We are to find the value of [tex]\cos \theta.[/tex]

We have the following trigonometric identity :

[tex]\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\sin^2\theta}\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\dfrac{9}{16}}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{\dfrac{7}{16}}\\\\\\\Rightarrow \cos \theta=\pm\dfrac{\sqrt{7}}{4}.[/tex]

Since [tex]\theta[/tex] lies in the first quadrant, so cosine of [tex]\theta[/tex] will be positive.

Thus,

[tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

A basketball player makes 175 out of 220 free throws. we would estimate the probability that the player makes the next free throw to be

Answers

80%, I divided 175 by 220 and got .795 which rounds up to 80%

The probability that the player will make next free throw is obtained as 0.795.

What is probability?

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The total number of free throws is 220.

And, the number of throws by the player is 175.

Now, the probability can be found as below,

P(free throws) = Throws by the Player ÷ Total throws

⇒ 175 ÷ 220 = 0.795

Hence, the probability for the next free throw can be estimated as 0.795.

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